Method 1: price per unit
$4.991.5 kg$3.33/kg
vs
$1.700.5 kg$3.40/kg
The lower price per kilogram is better value.
Chapter 16
Money
Compare prices fairly, identify the best value, and convert between currencies confidently by understanding exactly what an exchange rate means.
By the end of this chapter, you should be able to
- compare products or offers using a common unit price;
- compare value by finding how much product you receive for each unit of money;
- recognise when a direct comparison is quicker than calculating unit prices;
- interpret an exchange rate correctly;
- decide whether to multiply or divide when converting currencies;
- compare prices quoted in different currencies and use two exchange rates together.
1
Subtopic 1
Value for money
The largest pack or the cheapest-looking offer is not automatically the best value. To compare fairly, put the options on the same basis.
Method 2: amount per unit of money
1500 g499 cents3.01 g/cent
vs
500 g170 cents2.94 g/cent
The greater amount per cent or dollar is better value.
Two reliable methods
\[\text{price per unit}=\frac{\text{price}}{\text{quantity}}\qquad\text{or}\qquad\text{quantity per unit of money}=\frac{\text{quantity}}{\text{price}}\]Always convert quantities to the same unit before comparing.
Are the pack sizes exact multiples?Yes
Direct comparison may be quickest.
If notUse a common unit
Compare $/kg, cents/100 g, $/L, ml/$, etc.
Worked example · Easy
Compare price per litre
5 litres of water cost $1.35. A 2-litre bottle costs $0.58. Which is better value?
5-litre option:
\[1.35\div5=0.27\text{ dollars per litre}\]2-litre option:
\[0.58\div2=0.29\text{ dollars per litre}\]Because $0.27 per litre is lower, the \(\boxed{5\text{-litre option}}\) is better value.
Worked example · Medium
Mixed units
A 750 g packet costs $2.64. A 1.2 kg packet costs $4.08. Which is better value?
Convert 750 g to 0.75 kg.
\[2.64\div0.75=3.52\text{ dollars/kg}\]\[4.08\div1.2=3.40\text{ dollars/kg}\]The 1.2 kg packet costs less per kilogram, so it is \(\boxed{\text{better value}}\).
Worked example · Medium
Use a direct multiple
A 500 g cereal pack costs $1.70. A 1.5 kg pack costs $4.99. Compare the prices without finding unit prices.
1.5 kg is three times 500 g.
\[3\times1.70=5.10\]Three small packs would cost $5.10, but the large pack costs $4.99.
So the \(\boxed{1.5\text{ kg pack}}\) is better value.
Worked example · Exam-style
Special offers can change with quantity
Shop A sells T-shirts at $7.99 each, with “buy two, get a third free”. Shop B sells T-shirts for $5.50 each if you buy two or more. Which shop is cheaper for a) 3 T-shirts and b) 4 T-shirts?
3 T-shirts:
\[\text{Shop A}=2\times7.99=15.98\]\[\text{Shop B}=3\times5.50=16.50\]So Shop A is cheaper for 3.
4 T-shirts:
\[\text{Shop A}=15.98+7.99=23.97\]\[\text{Shop B}=4\times5.50=22.00\]So Shop B is cheaper for 4.
Worked example · Exam-style
Compare multi-packs
Pack X contains 12 cans of 150 ml for $5.40. Pack Y contains 6 cans of 330 ml for $3.24. Which gives more drink for each dollar?
Pack X volume:
\[12\times150=1800\text{ ml}\]\[1800\div5.40=333.33\ldots\text{ ml per dollar}\]Pack Y volume:
\[6\times330=1980\text{ ml}\]\[1980\div3.24=611.11\ldots\text{ ml per dollar}\]So \(\boxed{\text{Pack Y}}\) gives more drink for each dollar and is better value.
High-grade check
If you compare price per unit, lower is better. If you compare quantity per dollar, higher is better. Do not reverse the conclusion.
Remember for this subtopic
Value for money compares the SAME quantity. Divide price by mass, volume or number of items, e.g. dollars per kilogram. Promotions require evaluating the number of packs actually bought, not just the advertised saving.
Worked example · Exam-style
Special-offer unit-price comparison
Shop A sells three 400 g packets for $7.20. Shop B sells a 1 kg packet for $5.70. Which is better value by cost per kilogram?
Step-by-step solution
Shop A: 1.2 kg for $7.20 gives \(7.20/1.2=\$6.00\)/kg. Shop B: \(\$5.70\)/kg. Shop B is cheaper by \(\boxed{\$0.30\text{/kg}}\).
Progressive practice: confidence to exam-style
Try each question before opening the solution. Exam-style questions are original and modelled on the skills tested in examinations.
1Easy practice [1 marks]
250 g of cereal costs $1.50. Find the price per kg.
Show Answer
Step-by-step solution
1 kg contains 4 lots of 250 g. Cost = 4×$1.50 = $6.00 per kg.
2Medium practice [2 marks]
A 2 L juice bottle costs $3.80 and a 1.5 L bottle costs $3.15. Which costs less per litre?
Show Answer
Step-by-step solution
2 L: $3.80/2 = $1.90/L. 1.5 L: $3.15/1.5 = $2.10/L. 2 L bottle is better value.
3Medium practice [3 marks]
A pack of 12 pencils costs $4.80. Find the cost per pencil.
Show Answer
Step-by-step solution
\(4.80\div12=\boxed{\$0.40}\) each.
4Exam-style practice [4 marks]
A shop offers 3 for the price of 2 on bottles normally costing $2.40. A rival sells six bottles for $10.20. Which is cheaper for six bottles, and by how much?
Show Answer
Step-by-step solution
Offer shop: pay for 4 bottles: 4×$2.40=$9.60. Rival=$10.20. Offer shop is cheaper by $0.60.
2
Subtopic 2
Currency conversion
An exchange rate tells you how much of one currency is equivalent to one unit of another currency. Exchange rates change, so always use the rate given in the question.
If $1 = €0.88
US dollars$135
× 0.88to euros
euros€118.80
euros€340
÷ 0.88to dollars
US dollars$386.36
How to decide: multiply or divide?
If \(1A=rB\):
- from A to B, multiply by \(r\);
- from B to A, divide by \(r\).
Then check whether the numerical size makes sense. If $1 = €0.88, a given amount in dollars will convert to fewer euros, while a given amount in euros will convert to more dollars.
Worked example · Easy
Multiply in the stated direction
The exchange rate is $1 = €0.88. Convert $135 to euros.
\[135\times0.88=118.8\]
Money is normally written to two decimal places:
\(\boxed{€118.80}\)
Worked example · Medium
Convert in the reverse direction
The exchange rate is $1 = €0.88. Convert €340 to dollars.
We are going backwards through the stated rate, so divide:
\[340\div0.88=386.3636\ldots\]To the nearest cent: \(\boxed{\$386.36}\).
Worked example · Medium
Rupees and dollars
The exchange rate is 1 USD = 101.50 PKR. Convert 24 360 PKR to US dollars.
PKR is on the right-hand side of the rate, so divide by 101.50.
\[24360\div101.50=240\]\(\boxed{\$240.00}\)
Using two exchange rates
€1
× \(\frac{2.08}{1.35}\)
SGD
If £1 = €1.35 and £1 = 2.08 Singapore dollars, both rates share the same base currency (£). This lets you build a euro-to-SGD conversion.
Worked example · Exam-style
Compare a local and overseas purchase
A laptop costs 54 500 PKR locally. Online it costs $450 plus $80 delivery. The exchange rate is 1 USD = 101.50 PKR. Which option is cheaper and by how much in PKR?
Online total:
\[450+80=530\text{ USD}\]Convert to PKR:
\[530\times101.50=53795\text{ PKR}\]Difference:
\[54500-53795=705\text{ PKR}\]The \(\boxed{\text{online option}}\) is cheaper by \(\boxed{705\text{ PKR}}\).
Worked example · Exam-style
Cross-currency rate
£1 = €1.35 and £1 = 2.08 Singapore dollars. Assuming proportional exchange rates, how many Singapore dollars are equal to €1?
€1.35 and SGD 2.08 are both equal to £1.
\[€1=\frac{2.08}{1.35}\text{ SGD}=1.540740\ldots\text{ SGD}\]So \(\boxed{€1\approx1.54\text{ SGD}}\).
Money answers
When the answer represents ordinary money, give two decimal places unless the currency normally uses whole units in the context or the question tells you otherwise.
Remember for this subtopic
If 1 unit of currency A equals \(r\) units of B, multiply A by \(r\) to get B. Divide B by \(r\) for the reverse direction. Apply any fee after checking how it is specified.
Worked example · Exam-style
Exchange rate with a fee
One dollar is worth 0.80 euros. A traveller exchanges $375, and the company deducts a flat €4 fee from the euros supplied. How many euros are received?
Step-by-step solution
Convert: \(375\times0.80=\text{€}300\). Deduct fee: \(300-4=\boxed{\text{€}296}\).
Progressive practice: confidence to exam-style
Try each question before opening the solution. Exam-style questions are original and modelled on the skills tested in examinations.
1Easy practice [1 marks]
If $1 = €0.90, convert $80 into euros.
Show Answer
Step-by-step solution
\(80\times0.90=\boxed{\text{€}72}\).
2Medium practice [2 marks]
If £1 = $1.25, convert $100 into pounds.
Show Answer
Step-by-step solution
\(100\div1.25=\boxed{\text{£}80}\).
3Medium practice [3 marks]
If €1 = 1.10 dollars, find the dollar value of €250.
Show Answer
Step-by-step solution
\(250\times1.10=\boxed{\$275}\).
4Exam-style practice [4 marks]
$1 = €0.80 and €1 = 4.50 units of currency X. How much X is obtained for $100?
Show Answer
Step-by-step solution
First $100→€80. Then €80×4.50 = 360 units of X.
Chapter 16 practice
Start with unit-price comparisons, then move to special offers, exchange rates and cross-currency reasoning. Keep answers hidden until you have attempted each question.
A. Build confidence: value for money
1Water bottles[3 marks]
Which is better value: 5 litres of water for $1.29 or 2 litres for $0.87?
Show Answer
5 L option:
\[1.29\div5=0.258\text{ dollars/L}\]2 L option:
\[0.87\div2=0.435\text{ dollars/L}\]The 5 L option has the lower price per litre, so \(\boxed{5\text{ litres for }\$1.29}\) is better value.
2Different masses[4 marks]
An 800 g loaf costs $0.96. A 1.2 kg loaf costs $1.41. Which is better value?
Show Answer
800 g = 0.8 kg.
\[0.96\div0.8=1.20\text{ dollars/kg}\]\[1.41\div1.2=1.175\text{ dollars/kg}\]The 1.2 kg loaf is cheaper per kilogram, so it is \(\boxed{\text{better value}}\).
3Shaving gel[4 marks]
A 75 ml bottle costs $2.38 and a 200 ml bottle costs $5.78. Which is better value?
Show Answer
Price per ml:
\[2.38\div75=0.03173\ldots\]\[5.78\div200=0.0289\]The 200 ml bottle has the lower price per ml, so \(\boxed{\text{the 200 ml bottle}}\) is better value.
4Compare offers[4 marks]
Restaurant A charges $12.50 for a meal and offers the second meal at half price. Restaurant B charges $9.50 per meal. Which is cheaper for two people?
Show Answer
Restaurant A:
\[12.50+6.25=18.75\]Restaurant B:
\[2\times9.50=19.00\]\(\boxed{\text{Restaurant A}}\) is cheaper by \(\boxed{\$0.25}\).
5Multi-pack comparison[5 marks]
Pack A contains 12 × 150 ml cans for $5.90. Pack B contains 6 × 330 ml cans for $3.18. Which gives more drink per dollar?
Show Answer
Pack A volume = \(12\times150=1800\) ml.
\[1800\div5.90=305.08\ldots\text{ ml/\$}\]Pack B volume = \(6\times330=1980\) ml.
\[1980\div3.18=622.64\ldots\text{ ml/\$}\]\(\boxed{\text{Pack B}}\) gives more drink per dollar.
B. Currency conversion
6USD to PKR[3 marks]
1 USD = 101.42 PKR. Convert $240 to Pakistani rupees.
Show Answer
\[240\times101.42=\boxed{24340.80\text{ PKR}}\]
7PKR to USD[3 marks]
Using 1 USD = 101.42 PKR, convert 3500 PKR to US dollars.
Show Answer
\[3500\div101.42=34.510\ldots\]
\(\boxed{\$34.51}\) to the nearest cent.
8EUR to AED[3 marks]
1 EUR = 4.16 AED. Convert €280 to dirhams.
Show Answer
\[280\times4.16=\boxed{1164.80\text{ AED}}\]
9AED to EUR[3 marks]
Using 1 EUR = 4.16 AED, convert 850 AED to euros.
Show Answer
\[850\div4.16=204.3269\ldots\]
\(\boxed{€204.33}\)
C. Exam-style challenge
10Changing back at a different rate[5 marks]
A traveller changes 1250 AUD into Japanese yen at 1 AUD = 91.89 JPY. How many yen does she receive?
Show Answer
\[1250\times91.89=\boxed{114862.5\text{ JPY}}\]
This would normally be written as approximately \(\boxed{114863\text{ JPY}}\) if whole yen are required.
11Reverse conversion[5 marks]
She later changes 15 000 JPY back to AUD when 1 AUD = 93.15 JPY. How many Australian dollars does she receive?
Show Answer
\[15000\div93.15=161.0305\ldots\]
\(\boxed{161.03\text{ AUD}}\)
12Overseas purchase[6 marks]
A laptop costs 54 500 PKR locally. Online it costs $450 plus $80 delivery. The rate is 1 USD = 101.50 PKR. Find the cheaper option and the difference in PKR.
Show Answer
Online price:
\[450+80=530\text{ USD}\]\[530\times101.50=53795\text{ PKR}\]Difference:
\[54500-53795=705\text{ PKR}\]\(\boxed{\text{Online is cheaper by 705 PKR}}\).
13Cross rate[6 marks]
£1 = €1.35 and £1 = 2.08 Singapore dollars. How many Singapore dollars are equivalent to €1?
Show Answer
€1.35 = SGD 2.08.
\[€1=\frac{2.08}{1.35}=1.540740\ldots\text{ SGD}\]\(\boxed{1.54\text{ SGD}}\) to 2 decimal places.
14Camera price in another currency[6 marks]
Using £1 = €1.35 and £1 = 2.08 Singapore dollars, find the cost in euros of a camera costing 240 Singapore dollars.
Show Answer
First convert SGD to pounds:
\[240\div2.08=115.3846\ldots\text{ GBP}\]Then pounds to euros:
\[115.3846\ldots\times1.35=155.7692\ldots\]\(\boxed{€155.77}\)
15Best-value reasoning[6 marks]
A 680 g block of cheese costs $5.18 and a 500 g block costs $3.98. Which is better value, and by how much per kilogram?
Show Answer
\[5.18\div0.680=7.6176\ldots\text{ dollars/kg}\]\[3.98\div0.500=7.96\text{ dollars/kg}\]
The 680 g block is better value.
\[7.96-7.6176\ldots=0.34235\ldots\]It is cheaper by about \(\boxed{\$0.34\text{ per kg}}\).
16Two-stage comparison[7 marks]
A product costs €84 in one country and $96 in another. The rate is $1 = €0.88. Which price is lower and by how much in euros?
Show Answer
Convert $96 to euros:
\[96\times0.88=€84.48\]Compare €84 with €84.48.
The \(\boxed{€84\text{ price}}\) is lower by \(\boxed{€0.48}\).
Chapter 16 high-grade checklist
Same units first
I convert kg/g or L/ml before comparing prices.
Unit price
I know that lower price per kg, litre or item means better value.
Amount per money
I know that a higher amount per dollar or cent means better value.
State the conclusion
I always say which option is better, not just show calculations.
Exchange direction
I use the stated rate to decide whether to multiply or divide, then check whether the numerical size makes sense.
Money accuracy
I normally give ordinary money answers to two decimal places and use the currency symbol/unit requested.